Solve 2/9 + 3/9: Adding Fractions with Common Denominators

Q: Why don't I add the denominators together?

The denominator tells you what size pieces you're working with. Since both fractions are ninths, you're adding pieces of the same size. Adding denominators would change the piece size, giving a wrong answer!

Q: What if the denominators were different?

If denominators are different, you first need to find equivalent fractions with the same denominator. Only then can you add the numerators. This problem is easier because denominators already match!

Q: How can I visualize this problem?

Think of a pizza cut into 9 equal slices. You have 2 slices plus 3 more slices. That gives you 5 slices out of the same 9-slice pizza!

Q: Can I use this method for any fractions with same denominators?

Yes! This rule works for any fractions with identical denominators: $ \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} $. Just add the numerators and keep the denominator.

Adding Fractions with Same Denominators

$\frac{2}{9}+\frac{3}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's color the appropriate number of squares, according to the given data

00:15 Now let's count and add to the numerator in the new fraction

00:21 The denominator equals the number of cells we divided

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{9}+\frac{3}{9}=$

Step-by-step solution

To solve the given problem, follow these steps:

Step 1: Verify that both fractions have the same denominator.
In this case, $\frac{2}{9}$ and $\frac{3}{9}$ both have a denominator of 9.
Step 2: Add the numerators of the fractions.
This results in $2 + 3 = 5$ .
Step 3: Keep the denominator the same.
Thus, the sum is $\frac{5}{9}$ .

Therefore, the solution to the problem is $\frac{5}{9}$ .

Final Answer

$\frac{5}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add only the numerators together
Technique: Add numerators: 2 + 3 = 5, keep denominator 9
Check: Verify answer makes sense: $\frac{5}{9}$ is between $\frac{2}{9}$ and $\frac{3}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators: $\frac{2}{9} + \frac{3}{9} = \frac{5}{18}$ is wrong! This creates a different fraction entirely. Always keep the common denominator unchanged and add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

The denominator tells you what size pieces you're working with. Since both fractions are ninths, you're adding pieces of the same size. Adding denominators would change the piece size, giving a wrong answer!

What if the denominators were different?

If denominators are different, you first need to find equivalent fractions with the same denominator. Only then can you add the numerators. This problem is easier because denominators already match!

How can I visualize this problem?

Think of a pizza cut into 9 equal slices. You have 2 slices plus 3 more slices. That gives you 5 slices out of the same 9-slice pizza!

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{5}{9}$ cannot be simplified further because 5 and 9 share no common factors except 1.

Can I use this method for any fractions with same denominators?

Yes! This rule works for any fractions with identical denominators: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ . Just add the numerators and keep the denominator.

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